1. Field of the Invention
This invention relates to a robot having a plurality of movable sections such as legs and a method of controlling the attitude of such a robot. More particularly, the present invention relates to a robot that autonomously maintains the stability of its attitude according to a predetermined stability criteria and a method of controlling the attitude of such a robot.
To be more specific, this invention relates to a robot that controls the stability of the attitude of its body without using a ZMP (zero moment point) as stability criteria and a method of controlling the attitude of such a robot. More particularly, it relates to a robot that controls the stability of the attitude of its body by paying attention to periodic motions of the moving parts thereof and a method of controlling the attitude of such a robot.
This application claims priority of Japanese Patent Application No. 2003-300521, filed on Aug. 25, 2003, and Japanese Patent Application No. 2004-234022, filed on Aug. 11, 2004, the entireties of which are incorporated by reference herein.
2. Description of the Related Art
A machine device adapted to move in a manner resembling to motions of human being by means of electric and/or magnetic operations is referred to as “robot”. It is said that the word “robot” derives from a Slavic word “ROBOTA (slave machine)”.
In Japan, robots started to become popular in the late 1960s, although many of them were industrial robots such as manipulators and transfer robots installed for the purpose of automating productive operations of factories and saving man power. Research and development efforts have been paid in recent years on mobile robots that are equipped with movable legs and adapted to work on legs. Expectations are high for such mobile robots in practical applications. Two-legged mobile robots modeled after human motions are referred to humanoid robots.
While two-legged robots that are based on human's biped locomotion are accompanied by problems of instability and difficulty of attitude control and walk control if compared with crawler type robots and four-legged or six-legged robots, they provide advantages including that they can adapt themselves to unleveled ground, walking surfaces with obstacles and undulations on the way and discontinued walling surfaces such as staircases and ladder to be stepped up and down so that they can move in a flexible manner.
Numerous techniques have already been proposed with regard to attitude control and stable walking of two-legged mobile robots. Stable “walking” as used herein is defined as “moving by using legs without stumbling and falling”. When the body of a robot stumbles and falls, it means that the ongoing operation of the robot is suspended and that considerable power and time need to be spent for the robot to stand up from the failing state and resume its operation. Additionally, when the robot stumbles and falls, there arises a risk that the robot itself and/or the object that the falling robot collides with can be fatally damaged. Thus, the attitude/stability control of robots for avoiding stumbling and falling is one of the priority issues when developing two-legged mobile robots.
The standing posture of a robot that is based on human's biped locomotion is unstable as basic attitude. A ZMP (zero moment point) is often used as a criteria for the stability of walking of a two-legged mobile robot. The evaluation of the stability of walking using a ZMP is based on d'Alembert's principle that the gravity and the inertial force exerted by a walking system on the floor surface and their moments are balanced respectively by the reaction force of the floor exerted by the floor surface to the walking system and its moment. As a consequence of reasoning in the framework of dynamics, there exists a point where both the pitch axis moment and the roll axis moment are equal to zero, or a ZMP, on one of the sides of the supporting polygon (or the ZMP-stable region) formed by the contact points of the soles relative to the floor and the floor surface or in the inside thereof (see, inter alia, Non-Patent Reference Document 1).
Generation of a bipedal walk pattern on the basis of the ZMP criteria provides advantages including that it is possible to define a sole landing point in advance and that it is easy to consider kinetic constraints for the tips of the feet corresponding to the profile of the floor surface. Additionally, using a ZMP for the evaluation of stability means that it is not force but a trajectory of motion that is handled as target for controlling the motion and hence it is technically more feasible.
Target ZMP control has been successful on real robots when motions are planned so as to achieve dynamic balance at each and every moment. The motion generation technique using a ZMP as stability criteria can realize stable bipedal walking and hence is a proven technique. On the other hand, in an aspect, stability control on the basis of a ZMP is constantly being restricted by a single equation and hence it is necessary to accurately model the robot itself and the environment in order to plan a trajectory of motion according to the ZMP criteria and constantly make the plan match the environment model to realize a robot motion by means of a high precision trajectory tracking control system. In other words, stability control on that basis of a ZMP is accompanied by a problem of adaptability to unknown environment. The operation of solving the ZMP equation entails a relatively heavy calculation cost and hence difficulties in real time control situations.
Satisfying the ZMP equation is a sufficient condition and not a necessary condition for attitude stability control of robot. It will be appreciated that human walk is not necessarily always maximizing the ZMP stability margin.
On the other hand, man walks humanly with the biological mechanism he has, appropriately utilizing the passive dynamics of the limbs without relying on a ZMP. If a robot can smartly utilize the passive dynamics, it may be possible to realize a walking motion with a high energy conversion efficiency, requiring neither an exquisitely designed model (and hence a heavy calculation cost of computing operations) nor a large drive torque of actuators.
For example, it is possible to take a walking motion for a periodic motion and at least part of each movable section of a robot for a physical oscillator. Then, it will be possible to control the walking motion of robot by determining or controlling the phase and the frequency of oscillation of the oscillator. When such a periodic motion continues, it may be taken for “a stable walk”. If there is a moment in a period when the dynamic balance and hence the stability are lost (according to the ZMP theory), it is possible to continue the walking motion so long as the stable limit cycle is restored by repeating the period. Furthermore, if the stable limit cycle is not restored in a period, the motion can be continued so long as the motion is converged to a constant periodic motion within a realistic period of time.
If stability is defined as such by paying attention to the walking motion of robot, it will be possible to realize “comprehensive stability” because a steady state is restored within several periods if the robot is exposed to an unknown external disturbance. Then, as a result, neither a precise model nor a precise trajectory tracking control is required. Additionally, the gain of the actuator can be reduced to make it possible to reduce the cost and improve the stability with a small gain. (Differently stated, if a precise model and a precise trajectory tracking control are required, the cost will rise due to the large gain and the precision). Furthermore, from the viewpoint of comprehensive, the robot is allowed to go out of a stable region. Then, walk and other leg motions (attitudes) can be realized in a variety of modes to raise the expression potential of the robot and improve the adaptability to the environment.
Walking techniques of legged mobile robot that pay attention to the periodicity of walking motion include biologically inspired adaptive dynamic walking of a quadruped robot on irregular terrain (see, inter alia, Non-Patent Reference Document 2) and the relationship between rhythm resetting against an external disturbance and dynamic stability of walk in a bipedal walking motion of man (see, inter alia, Non-Patent Reference Document 3).
According to the former document, an adaptive motion is creatively generated through interaction of a dynamic system formed by coupling a machine system and a nervous system on the basis of unique non-linear dynamics and the environment. However, the former document says that phase and frequency are entrained by a nonlinear differential equation (Matsuoka Oscillator) to reveal that it is not possible to obtain an analytic solution for the phase of the physical oscillator and hence mathematically design the system. In short, it is not possible to get to any specific design theory.
According to the latter document, it is possible to mathematically analyze the relationship between the trajectory of motion that involves phase resetting and dynamic stability by using a dynamics type model for a bipedal walking motion. However, it only describes regulation of the phase of the physical oscillator by way of an open loop immediately after a known external disturbance and lacks any feedback from the physical system and hence adaptability to unknown states and external disturbances.
[Non-Patent Reference Document 1] Miomir Vukobratovic, “LEGGED LOCOMOTION ROBOTS”, (Ichiro Kato et al., “A Walking Robot and Artificial Feet”, (Nikkan Kogyo Shinbun, Ltd.).
[Non-Patent Reference Document 2] Fukuoka et al., “Biologically Inspired Adaptive Dynamic Walking of a Quadruped on Irregular Terrain—Proposal of the Design of Coupled Neuro-Mechanical System and Evaluation of the Mutual Entrainment among Pitch Motion, CPG and Rolling Motion”, (Journal of Robotics Society in Japan, Vol. 21, No. 5, July 2003).
[Non-Patent Reference Document 3] Yamazaki et al., “The Relationship between Rhythm Resetting against an External Disturbance and Dynamic Stability of a Bipedal Walking Motion of Man”, (Technical Report of IEICE, The Institute of Electronics, Information and Communication Engineers).